Date: Feb 2, 2013 3:36 AM
Author: William Elliot
Subject: Re: closed but not complete

On Fri, 1 Feb 2013, Butch Malahide wrote:
> On Feb 1, 9:14 pm, William Elliot <ma...@panix.com> wrote:
> > On Fri, 1 Feb 2013, Daniel J. Greenhoe wrote:
> >

> > > Let (Y,d) be a subspace of a metric space (X,d).
> >
> > > If (Y,d) is complete, then Y is closed with respect to d. That is,
> > > complete==>closed.

> >
> > > Alternatively, if (Y,d) is complete, then Y contains all its limit
> > > points.


> > > Would anyone happen to know of a counterexample for the converse?
> > > That is, does someone know of any example that demonstrates that
> > > closed --> complete is *not* true?

> >
> > No. Assume K is a closed subset of the complete space (S,d).

>
> But the original poster did not say that his metric space (X,d) was
> complete.
>

Oh, so any closed subset of Q is an example.

Given that A subset Q, is open or closed,
what's the probablity that it's clopen?

Whops, here's the simple version. A subset of a linear
order is consider to be an interval when it's order convex.

Given an open or a closed interval of Q,
what's the probablity that it's clopen?